#15: Model Solves Fundamental Packing Problem

How do different-sized spheres fit into a large container?

By Stephen Ornes|Monday, January 25, 2010

The county-fair challenge of guessing how many gum balls are in a jar is far more than just a game for kids; understanding how objects pack into a particular volume is a fundamental problem of physics and engineering. A team of physicists at New York University recently loosened the problem a bit, producing a simple model that predicts the arrangement of randomly packed spherical particles, even when the objects are of different sizes.

Theorists had previously calculated that each particle touches an average of six neighbors, and that packed spheres of uniform size fill about 64 percent of the total available space. Jasna Brujic and colleagues experimentally verified both of those claims using a three-dimensional microscope—which examines many horizontal layers of a sample and then stacks those images to create a 3-D image—to analyze oil droplets tightly packed in water. The physicists also studied how changing the mix of droplet sizes affects their arrangement.

“If you give us the distribution of particle sizes, we can tell you about their geometry,” Brujic says. The research, published in Nature in July, could inspire better ways to stock vending machines, prepare products for shipping, grind drugs for pills, and extract petroleum from porous rocks. But so far Brujic has modeled only spheres; contestants dealing with gumdrops or M&M’s will have to wait for future studies.

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